Question

In this week's lesson, Week 2: Linear Equations, we explored four different linear relationships with respect to slope: positive, negative, zero, and undefined slopes. As you create your own example, think of the relationship between the independent variable (x) and dependent variable (y). Here's another quick example to help you construct your own linear scenario: Suppose you are painting a wall, and you begin with 5 gallons in the can. Graphically, 5 gallons would be our y-intercept for time at 0 hours (since we haven't started painting yet). Would the quantity of paint in the can increase or decrease as you transfer the paint from the can to the wall? What linear relationship does this example represent? If the gallons in the can decreased by one gallon every 30 minutes, can you predict when the can will run out of paint? Come up with your own word problem, don't forget to include at least two parts for your classmates to solve, and have your answer ready!

Answer 1

1.)

The quantity of paint in the can decreases as you transfer the paint from the can to wall

2.)

This linear relationship is y=mx+c which represent the quantity remaining in the can at time x after started painting.

3.)

at x=0, initially the quantity of paint in the can is y=5 gallons. i.e., 5=m(0)+c implies c=5. The relation is y=mx+5.

at x=30, after 30 minutes the quantity is decreased by 1 gallon. so at x=30 y=4 gallons. So, 4=m(30)+5 implies m=-1/30.

The linear relation is y=(-1/30)x+5.

4.)

the can will run out of paint when the quantity remaining in the can is zero.

i.e., 0=(-1/30)x+5 implies x(1/30)=5 implies x=150 minutes. i.e., x=2 hour 30 minutes. The can will run out of paint after 2 hour 30 minutes.